Hatters boss John Still is still waiting to see if club captain Ronnie Henry will sign a new deal at the club.
The 30-year-old, who lifted the Skrill Premier title this season, is currently out of contract at Kenilworth Road.
Still said: “We’ve made an offer to Ron, and we’re waiting for Ron’s reply.
“I would think there would be some sort of response to that by the end of this week.”
Town made their first move in the transfer market last week, signing another right-back, as Lowestoft’s Curtley Williams joined.
Still also confirmed there will be more signings over the summer, with Dulwich Hamlet’s Erhun Oztumer remaining a possibility.
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